Dennis is steering you correctly.
Most likely you are draining the radiator by opening the petcock at the bottom of the radiator rather than disconnecting the lower radiator hose.
On each side of the engine block, in front of each motor mount, below a 'soft plug', is located a petcock as well. Opening these two petcocks will drain the coolant in the intake manifold, each cylinder heads, and the engine block.
IF you desire, you can get still more coolant out of the system by disconnecting the heater hose where it connects at the top of the intake manifold and at the water pump. Move the two disconnected heater hoses to the passenger side of the engine and then lower them toward the oil pan so that they are lower than heater connection on the firewall. This will permit the draining of the hoses and the heater core.
Hope this helps!

Regards,
NoShortcuts
a.k.a. Charlie Brown
near Syracuse, New York